We previously reported that the 80-year-old Burstyn visited a two-bedroom, two-bathroom rental at 515 W. 23rd St. that was asking $12,000 a month.

And now Burstyn, who’s been in everything from “The Exorcist” to “Same Time, Next Year,” has just looked at an $11,000-a month residence at 343 W. 29th St.

This 2,400-square-foot, three-bedroom, 2 1/2-bathroom rental duplex is inside a landmarked 1847 townhouse in the Lamartine Place Historic District, which was once a stop on the city’s underground railroad.

The rental unit’s parlor-level entrance opens to a living/dining area and an eat-in chef’s kitchen. There are two gas fireplaces, and updates including central air conditioning and two Philippe Starck bathrooms. There’s also a bi-level private garden.

Apparel mogul Jason Rabin, the son of Brooklyn Nets co-owner Artie Rabin, is renting Ricky Martin’s former five-bedroom, $32,500-a-month apartment at the Lucida building on East 85th Street. “Modern Family” co-star Jesse Tyler Ferguson also lives in the condo complex.

Rabin, with his father, founded Wear Me Apparel — which designs and markets clothing brands for big department stores. The company was purchased by Li & Fung Limited, where Rabin is now president of an Asian subsidiary.

He and his wife, Nicole, recently sold a penthouse duplex at 23 E. 74th St. for $17.5 million. That unit was previously owned by Jane Holzer, known best as Andy Warhol’s “Baby Jane.”

Carmine could be yours for right price

In the market for a curious and exclusive piece of downtown real estate? A townhouse hidden behind a gate on a tiny West Village street has hit the market with a $3.55 million asking price.

The four-bedroom, 2 1/2-bathroom residence is in a “hidden enclave” on Carmine Street. The home, built in 1858, features a Dutch door that opens to a parlor floor with a woodburning fireplace in the living room. There’s an original mahogany banister, plus two more fireplaces on the second floor. The home is owned by Richard La Capra, an engineer, and his writer wife, Wendy. The brokers are Leslie Mason and Kevin Landers of Douglas Elliman.

Hamptons ‘show’ house

Recently widowed Roy Furman, the Broadway producer and finance guru/chairman of Jefferies Capital Partners, has put his Hamptons mansion on the market for $19.95 million.

The Amagansett home above Gardiners Bay was previously owned by Hollywood producer Barry Sonnenfeld and has one of the best screening rooms at the beach — described in the listing as a “Hollywood-size professional theater.” The Traditional-style, five-bedroom, 6 1/2-bathroom house with five fireplaces is 9,000 square feet and comes with a “separate but attached” two-bedroom staff apartment. There are also exercise and game rooms, a pool and three garages on 1.93 acres.

The listing agent is Diane Saatchi of Saunders. We hear that city broker Richard Steinberg of Warburg is also involved.

Diamond rocks the block with double deal

PR/marketing guru Harris Diamond has just doubled the size of his residence at 912 Fifth Ave.

He plunked down $7 million to purchase an apartment on the same floor as the $6.5 million unit he bought last year. Spies tell us that Diamond and his wife, Amy, are planning to create a full floor-through residence.

It’s all in a 1925, white-glove, 15-story co-op building, between East 72nd and East 73rd streets, with 31 units.

Diamond is chairman and CEO of McCann Worldgroup, which, according to its Web site, “spans over 120 countries.” The Diamonds also own a home in Weston, Conn.